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Phase velocity of an electron with kinetic energy of 5eV and 50keV

  1. Mar 25, 2008 #1
    1. The problem statement, all variables and given/known data
    Consider electrons of kinetic energy 5eV and 500keV. For each electron, what would be the
    particle speed, phase velocity, group velocity, and Broglie wavelength?

    2. Relevant equations
    lambda = h/p (lambda = broglie wavelength)
    K.E. for nonrelativistic calcualtion = p^2/(2m)
    phase velocity = lambda*f = lambda / time
    group velocity = dw/dk

    3. The attempt at a solution
    So for the 5eV case, I found that since the energy is low, i can use non-relativistic calculation. I find the Broglie wavelength to be around 0.548 nm and the momentum to be 1.208E-24 kg(m/s). Knowing the momentum, I used p=mv to find the particle velocity, which came out to be around 1.326E6 m/s.

    So far I think I am doing it right, but I cannot find the phase velocity nor the group velocity. Something tells me that for a non-relativistic case, the phase velocity is equal to c and the group velocity is equal to the particle speed. Can anyone explain this to me?

    Also, how should I approach the 50keV electron case, since the energy is so high I need to use relativity.

  2. jcsd
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